Question

The product of two numbers is 66. Their sum is 17. What are the two numbers?

Answer 1

ɢɪᴠᴇɴ :-

• Product of two numbers = 66
• Sum of two numbers = 17

Tᴏ ғɪɴᴅ :-

• Two numbers

sᴏʟᴜᴛɪᴏɴ :-

Let first no be x and second number be y

then,

➲ ᴄᴏɴᴅɪᴛɪᴏɴ -1

• First no × Second no = 66

• xy = 66 --(1)

➲ ᴄᴏɴᴅɪᴛɪᴏɴ -2

• First no + Second no = 17

• x + y = 17

• x = (17 - y) --(2)

Put the value of (2) in (1) , we get

➭ (17 - y) y = 6

➭ 17y - y² = 66

➭ y² - 17y + 66 = 0

➭ y² - 11y - 6y + 66 = 0

➭ y(y - 11) - 6(y - 11) = 0

➭ (y - 6)(y - 11) = 0

➭ y = 6 or y = 11

We get two different values of y so both values of y satisfy the conditions of question.

If we put y = 6 in (2) ,

➭ x + y = 17

➭ x + 6 = 17

➭ x = 17 - 6

➭ x = 11

If we put y = 11 in (2) ,

➭ x + y = 17

➭ x + 11 = 17

➭ x = 17 - 11

➭ x = 6

Therefore,

Either first no is 6 or 11 or second no is 6 or 11

So,

• First no = 6 or 11
• Second no = 6 or 11

This means if first no is 6 then second no is 11 or vice-versa

Answer 2

$\large\bf{\underline{Question:-}}$

The product of two numbers is 66. Their sum is 17. What are the two numbers?

$\large\bf{\underline{Given:-}}$

• Product of two number is 66.
• Their sum is 17.

$\large\bf{\underline{To \:find:-}}$

• Two numbers=?

$\large\bf{\underline{Solution:-}}$

$\tt→ Let \:the\: two \:numbers\: are\: A \:and \:B$

$\large\bf{\underline{According\:to\:Question:-}}$

$\tt→ ab=66\\\tt→ a+b=17---equ(1)$

$\tt By\: equation\:(1)$

$\tt→ (a-b)^2=(a+b)^2-4ab\\\tt→ (a-b)^2 = 17^2-4(66)\\\tt→ (a-b)^2= 289-264\\\tt→ (a-b)^2=25\\\tt→ a-b=\sqrt25\\\tt→ a-b=5----equ(2)$

$\tt\leadsto\:Solve\: equation\:(1)and\:(2)\\\tt\large→ we\:get,$

$\tt→ a+b=17\\\tt→ {\underline{a-b=5}}\\\tt→ 2a=22\\\tt→ a=11$

Now,

in given it is given that Sum of two number is 17.

$\tt→ a+b=17 (putting\:a=11\:in \: equation\:1)\\\tt→ 11+b=17\\\tt→b=17-11\\\tt→ b=6$

Hence,

the two number are 11 and 6